What “the most ordinary Snakes-and-Ladders” can do for the preschool math gap.
Introduction: The Math Gap Is Already Open Before School Starts
The moment children walk into kindergarten, they are not standing at the same starting line. A meta-analysis by Duncan and colleagues (2007) of six longitudinal studies found that math performance at school entry consistently predicts math achievement through elementary, middle, and high school. The relationship was much stronger than for reading (mean standardized beta .34 vs .16).
The harder problem is the income gap. On nonverbal magnitude or shape comparison tasks, low-income children perform at roughly the same level as higher-income peers. But the moment a task requires verbal numerical concepts — “Which is bigger, 9 or 4?”, “Where would 5 sit on this line?” — the gap widens dramatically.
If the gap were just “they didn’t practice counting enough,” the fix would be easy. But prior work has shown that even after a child can fluently count from 1 to 10, building a sense of numerical magnitude takes more than a year. “Reciting numbers” and “feeling the size of numbers” are different tasks.
So what creates this magnitude sense?
The Core Research Question
Carnegie Mellon and University of Maryland researchers (Ramani & Siegler) asked:
“Could playing a simple board game with a linear arrangement of numbers improve low-income preschoolers’ numerical knowledge in real ways? Would the effects last?”
Four predictions were tested:
- After playing the game, do children improve on all four numerical tasks (counting, numeral identification, magnitude comparison, number-line estimation)?
- Does the gain persist 9 weeks later?
- If you replace numbers with colors but otherwise keep the game identical, does the effect disappear?
- Is home board-game experience related to numerical knowledge?
What Game Was Played: “The Great Race”
The simple board the team designed is called “The Great Race”. Physically:
- 52 cm wide, 24 cm tall
- “Start” on the left, “End” on the right
- Ten same-sized squares arranged in a straight line between them
- Number version: each square labeled 1, 2, 3 … 10 in order
- Color version: same ten squares, each painted a different color
- Spinner: number version had “1” and “2” splits; color version showed colors matching the board
A child picks a rabbit or bear token, takes turns with the experimenter spinning, and moves their token. First to “End” wins.
The key rule: say the numbers as you move
The most important rule. If a child is on square 3 and spins a 2, they must say “4, 5!” while moving the token. They are not just moving “two squares forward” — they are reading the squares’ numbers as they pass them.
In the color version, spinning “blue” meant saying “red, blue” while moving.
The most common mistake was children counting “1, 2” — counting moves rather than reading squares. The experimenter would correct: “Read the numbers on the squares you’re passing.” This small rule is the hidden engine of the intervention.
Study Design and Participants
- Participants: 124 children from 10 Head Start centers (a U.S. early-education program serving low-income families)
- Age: 4 years 1 month – 5 years 5 months (mean 4 years 9 months)
- Income criterion: 3-person household income under $16,600 (below U.S. federal poverty line)
- Race: 50% African American, 43% Caucasian, 7% other
- Random assignment: 68 to the number board, 56 to the color board
- Schedule: 4 sessions across 2 weeks, each 15–20 minutes (~20 plays per session, ~2–4 minutes per game)
- Follow-up: 9-week retention
The four assessment tasks:
- Counting: count from 1 to 10; how many before the first error
- Number-line estimation: on a 25-cm line marked 0 and 10, mark the position of “5” and other numbers
- Magnitude comparison: “Which is bigger, 8 or 3?”
- Numeral identification: read aloud cards showing 1–10
Results: Meaningful Gains on All Four Tasks
Numeral identification
The number-board group went from 7.0 → 8.2 → 8.7 (pre → post → 9-week follow-up). The color-board group barely moved: 6.1 → 6.3 → 6.6. Effect sizes d = 0.44 (post), d = 0.63 (9-week).
Magnitude comparison
The number group improved from 73% → 85% → 83% accuracy; the color group: 68% → 70% → 70%. Effect size d = 0.79 — a striking improvement in “which is bigger.”
Counting
The number group went from 8.7 → 9.9 → 9.9, near ceiling. After play, 94% counted from 1 to 10 with zero errors, and 97% did so 9 weeks later. The color group reached only 71% and 77% at the same time points.
Number-line estimation (the most dramatic shift)
This task probes a child’s mental representation of the number line most directly. Before play, the number-board group’s estimates fit a linear function for an average of just 17% of variance — they couldn’t place big and small numbers in the right places. After play, 46%. Nine weeks later, still 34%. Effect size d = 1.00 — uncommonly large for a developmental experiment.
The color group: 15% → 16% → 18%. No change at all.
The strength of the control: why the color version did nothing
This study’s strongest design feature was the control. Children in the color group spent the same amount of time, with the same friendly adult experimenter, on the same-shaped board, moving tokens. Their numerical knowledge didn’t budge.
This rules out “fun time with an adult,” “test-retest practice,” “Head Start classroom learning,” and “the game itself was fun” as the cause. Only the act of moving along a linear arrangement of numbers, naming them aloud, drove the effect.
Why a Board Game, Not Counting Drills
The team’s theoretical core: counting numbers and arranging them by magnitude in your head are different abilities.
A linear board game offers multiple, mutually reinforcing cues to numerical magnitude. The bigger the number, (a) the farther the token has moved, (b) the more moves it took, (c) the more numbers spoken, (d) the more numbers heard, (e) the more time has passed since the start.
All these cues point in the same direction: “bigger number = farther, longer, more moves.” Visual, kinesthetic, auditory, and temporal cues all align. In this sense, the board game physically realizes the mental number line.
A simple counting drill provides only the rhythm “1, 2, 3…” — no spatial or quantitative experience between numbers. Indeed, Malofeeva et al. (2004) gave Head Start children intensive counting and numeral-identification practice; their counting and identification scores improved, but magnitude sense did not. Same children, same time, very different result. What you have them repeat decides the outcome.
Home Board-Game Experience and Numerical Knowledge
In Experiment 2, the team asked: outside the lab, does home board-game experience correlate with numerical knowledge?
Has played a board game at home:
- Middle-class children: 80%
- Head Start (low-income) children: 47%
Has played Chutes and Ladders (the classic linear-number board game):
- Middle-class: 37%
- Low-income: 17%
Conversely, video games:
- Middle-class: 30%
- Low-income: 66%
It wasn’t that low-income children played fewer games. They played fewer linear number board games.
Among Head Start children, more board-game experience correlated with higher scores on all four numerical tasks (r = .20 to .38). Card games and video games barely correlated. Just any game won’t do — the structure of the game matters.
Practical Implications
Board games over workbooks
This intervention requires no expensive materials. A piece of paper, a pencil, a coin. Draw a line, mark 1 to 10, label one side of a coin “1” and the other “2.” Twenty minutes per session, four sessions across two weeks. About an hour total — and the gains were still visible nine weeks later.
Have them say the numbers as they move
The hidden engine isn’t “moving the token” but reading the numbers on the squares they pass aloud. “If the child is on 3 and spins a 2, they say ‘4, 5’ while moving.” That action implants the sense that “4 and 5 sit farther than 3.” Counting moves (“1, 2”) drills counting, not magnitude.
Chutes and Ladders, not Candy Land
Color-based board games (like Candy Land) are loved by kids, but in this study’s context they don’t grow magnitude sense. A linear arrangement of numbers — Snakes and Ladders, number boards, numbered game tracks — is what counts.
Limitations
The team noted:
- The choice of “4 sessions” was somewhat arbitrary. Whether more produces more, or hits a ceiling, is unknown.
- The experimenters were highly motivated researchers. Whether parents or teachers produce the same effect wasn’t tested.
- Only 1:1 play was tested. Small-group effects need separate verification.
- Low-income children were the focus. Middle-class children — already higher in numerical knowledge — may show ceiling effects.
Closing
The message is simple:
The most ordinary play can be the most powerful early-math intervention.
A linear number board game physically simulates the process of building a mental number line. As the child moves a token square by square and names the numbers, hand movement, spoken sound, heard sound, and visual distance all point the same way — “bigger numbers are farther.”
You don’t need a desk to teach math. Sometimes you just need a sheet of paper, ten squares, and “first one to the end wins!” Children think it’s a game. It worked better than any curriculum the researchers had tried.
Source: Ramani, G. B., & Siegler, R. S. (2008). Promoting broad and stable improvements in low-income children’s numerical knowledge through playing number board games. Child Development, 79(2), 375–394. https://doi.org/10.1111/j.1467-8624.2007.01131.x